1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 440,741 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… miss… e380000… nhs_glo…     1 gl34fe   South West
##  2 111       2020-03-18 fema… miss… e380001… nhs_sou…     1 ne325nn  North Eas…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_air…     8 bd57jr   North Eas…
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_ash…     7 tn254ab  South East
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_bar…     9 n111np   London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    11 s752py   North Eas…
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_bas…    19 ss143hg  East of E…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_bas…     6 dn227xf  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_bat…     9 ba25rp   South West
## # … with 440,731 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##      date_report               nhs_region deaths
## 1     2020-03-01          East of England      0
## 2     2020-03-02          East of England      1
## 3     2020-03-03          East of England      0
## 4     2020-03-04          East of England      0
## 5     2020-03-05          East of England      0
## 6     2020-03-06          East of England      1
## 7     2020-03-07          East of England      0
## 8     2020-03-08          East of England      0
## 9     2020-03-09          East of England      1
## 10    2020-03-10          East of England      0
## 11    2020-03-11          East of England      0
## 12    2020-03-12          East of England      0
## 13    2020-03-13          East of England      1
## 14    2020-03-14          East of England      2
## 15    2020-03-15          East of England      2
## 16    2020-03-16          East of England      1
## 17    2020-03-17          East of England      1
## 18    2020-03-18          East of England      5
## 19    2020-03-19          East of England      4
## 20    2020-03-20          East of England      2
## 21    2020-03-21          East of England     11
## 22    2020-03-22          East of England     12
## 23    2020-03-23          East of England     11
## 24    2020-03-24          East of England     19
## 25    2020-03-25          East of England     26
## 26    2020-03-26          East of England     36
## 27    2020-03-27          East of England     38
## 28    2020-03-28          East of England     28
## 29    2020-03-29          East of England     43
## 30    2020-03-30          East of England     45
## 31    2020-03-31          East of England     70
## 32    2020-04-01          East of England     63
## 33    2020-04-02          East of England     65
## 34    2020-04-03          East of England     80
## 35    2020-04-04          East of England     71
## 36    2020-04-05          East of England     76
## 37    2020-04-06          East of England     71
## 38    2020-04-07          East of England     93
## 39    2020-04-08          East of England    111
## 40    2020-04-09          East of England     87
## 41    2020-04-10          East of England     74
## 42    2020-04-11          East of England     92
## 43    2020-04-12          East of England    100
## 44    2020-04-13          East of England     78
## 45    2020-04-14          East of England     61
## 46    2020-04-15          East of England     82
## 47    2020-04-16          East of England     74
## 48    2020-04-17          East of England     86
## 49    2020-04-18          East of England     64
## 50    2020-04-19          East of England     67
## 51    2020-04-20          East of England     67
## 52    2020-04-21          East of England     75
## 53    2020-04-22          East of England     67
## 54    2020-04-23          East of England     49
## 55    2020-04-24          East of England     66
## 56    2020-04-25          East of England     54
## 57    2020-04-26          East of England     48
## 58    2020-04-27          East of England     46
## 59    2020-04-28          East of England     58
## 60    2020-04-29          East of England     32
## 61    2020-04-30          East of England     45
## 62    2020-05-01          East of England     49
## 63    2020-05-02          East of England     29
## 64    2020-05-03          East of England     41
## 65    2020-05-04          East of England     19
## 66    2020-05-05          East of England     36
## 67    2020-05-06          East of England     31
## 68    2020-05-07          East of England     33
## 69    2020-05-08          East of England     33
## 70    2020-05-09          East of England     29
## 71    2020-05-10          East of England     22
## 72    2020-05-11          East of England     18
## 73    2020-05-12          East of England     21
## 74    2020-05-13          East of England     27
## 75    2020-05-14          East of England     26
## 76    2020-05-15          East of England     19
## 77    2020-05-16          East of England     26
## 78    2020-05-17          East of England     17
## 79    2020-05-18          East of England     25
## 80    2020-05-19          East of England     15
## 81    2020-05-20          East of England     26
## 82    2020-05-21          East of England     21
## 83    2020-05-22          East of England     13
## 84    2020-05-23          East of England     12
## 85    2020-05-24          East of England     17
## 86    2020-05-25          East of England     25
## 87    2020-05-26          East of England     14
## 88    2020-05-27          East of England     12
## 89    2020-05-28          East of England     17
## 90    2020-05-29          East of England     16
## 91    2020-05-30          East of England      9
## 92    2020-05-31          East of England      8
## 93    2020-06-01          East of England     17
## 94    2020-06-02          East of England     14
## 95    2020-06-03          East of England     10
## 96    2020-06-04          East of England      7
## 97    2020-06-05          East of England     14
## 98    2020-06-06          East of England      5
## 99    2020-06-07          East of England      9
## 100   2020-06-08          East of England      7
## 101   2020-06-09          East of England      6
## 102   2020-06-10          East of England      8
## 103   2020-06-11          East of England      1
## 104   2020-06-12          East of England      9
## 105   2020-06-13          East of England      5
## 106   2020-06-14          East of England      4
## 107   2020-06-15          East of England      8
## 108   2020-06-16          East of England      3
## 109   2020-06-17          East of England      7
## 110   2020-06-18          East of England      4
## 111   2020-06-19          East of England      7
## 112   2020-06-20          East of England      4
## 113   2020-06-21          East of England      3
## 114   2020-06-22          East of England      6
## 115   2020-06-23          East of England      5
## 116   2020-06-24          East of England      4
## 117   2020-06-25          East of England      1
## 118   2020-06-26          East of England      5
## 119   2020-06-27          East of England      6
## 120   2020-06-28          East of England      8
## 121   2020-06-29          East of England      4
## 122   2020-06-30          East of England      5
## 123   2020-07-01          East of England      2
## 124   2020-07-02          East of England      5
## 125   2020-07-03          East of England      0
## 126   2020-07-04          East of England      3
## 127   2020-07-05          East of England      1
## 128   2020-07-06          East of England      2
## 129   2020-07-07          East of England      2
## 130   2020-07-08          East of England      0
## 131   2020-07-09          East of England      8
## 132   2020-07-10          East of England      4
## 133   2020-07-11          East of England      2
## 134   2020-07-12          East of England      1
## 135   2020-07-13          East of England      8
## 136   2020-07-14          East of England      2
## 137   2020-07-15          East of England      0
## 138   2020-07-16          East of England      0
## 139   2020-07-17          East of England      0
## 140   2020-07-18          East of England      0
## 141   2020-07-19          East of England      1
## 142   2020-07-20          East of England      1
## 143   2020-07-21          East of England      1
## 144   2020-07-22          East of England      2
## 145   2020-07-23          East of England      1
## 146   2020-07-24          East of England      1
## 147   2020-07-25          East of England      0
## 148   2020-07-26          East of England      1
## 149   2020-07-27          East of England      1
## 150   2020-07-28          East of England      2
## 151   2020-07-29          East of England      0
## 152   2020-07-30          East of England      0
## 153   2020-07-31          East of England      1
## 154   2020-08-01          East of England      0
## 155   2020-08-02          East of England      0
## 156   2020-08-03          East of England      0
## 157   2020-08-04          East of England      1
## 158   2020-08-05          East of England      1
## 159   2020-08-06          East of England      0
## 160   2020-08-07          East of England      1
## 161   2020-08-08          East of England      0
## 162   2020-08-09          East of England      0
## 163   2020-08-10          East of England      1
## 164   2020-08-11          East of England      2
## 165   2020-08-12          East of England      1
## 166   2020-08-13          East of England      0
## 167   2020-08-14          East of England      1
## 168   2020-08-15          East of England      1
## 169   2020-08-16          East of England      0
## 170   2020-08-17          East of England      0
## 171   2020-08-18          East of England      2
## 172   2020-08-19          East of England      1
## 173   2020-08-20          East of England      1
## 174   2020-08-21          East of England      0
## 175   2020-08-22          East of England      1
## 176   2020-08-23          East of England      1
## 177   2020-08-24          East of England      0
## 178   2020-08-25          East of England      0
## 179   2020-08-26          East of England      1
## 180   2020-08-27          East of England      1
## 181   2020-08-28          East of England      0
## 182   2020-08-29          East of England      0
## 183   2020-08-30          East of England      0
## 184   2020-08-31          East of England      0
## 185   2020-09-01          East of England      0
## 186   2020-09-02          East of England      0
## 187   2020-09-03          East of England      1
## 188   2020-09-04          East of England      1
## 189   2020-09-05          East of England      0
## 190   2020-09-06          East of England      1
## 191   2020-09-07          East of England      0
## 192   2020-09-08          East of England      0
## 193   2020-09-09          East of England      0
## 194   2020-09-10          East of England      0
## 195   2020-09-11          East of England      0
## 196   2020-09-12          East of England      0
## 197   2020-09-13          East of England      1
## 198   2020-09-14          East of England      1
## 199   2020-09-15          East of England      0
## 200   2020-09-16          East of England      0
## 201   2020-09-17          East of England      0
## 202   2020-09-18          East of England      0
## 203   2020-09-19          East of England      0
## 204   2020-09-20          East of England      2
## 205   2020-09-21          East of England      0
## 206   2020-09-22          East of England      2
## 207   2020-09-23          East of England      1
## 208   2020-09-24          East of England      0
## 209   2020-09-25          East of England      1
## 210   2020-09-26          East of England      1
## 211   2020-09-27          East of England      1
## 212   2020-09-28          East of England      2
## 213   2020-09-29          East of England      2
## 214   2020-09-30          East of England      2
## 215   2020-10-01          East of England      2
## 216   2020-10-02          East of England      1
## 217   2020-10-03          East of England      1
## 218   2020-10-04          East of England      0
## 219   2020-10-05          East of England      0
## 220   2020-10-06          East of England      4
## 221   2020-10-07          East of England      6
## 222   2020-10-08          East of England      3
## 223   2020-10-09          East of England      1
## 224   2020-10-10          East of England      6
## 225   2020-10-11          East of England      2
## 226   2020-10-12          East of England      2
## 227   2020-10-13          East of England      1
## 228   2020-10-14          East of England      3
## 229   2020-10-15          East of England      4
## 230   2020-10-16          East of England      5
## 231   2020-10-17          East of England      6
## 232   2020-10-18          East of England      7
## 233   2020-10-19          East of England      5
## 234   2020-10-20          East of England      9
## 235   2020-10-21          East of England      7
## 236   2020-10-22          East of England      7
## 237   2020-10-23          East of England     14
## 238   2020-10-24          East of England      1
## 239   2020-10-25          East of England     10
## 240   2020-10-26          East of England     10
## 241   2020-10-27          East of England      8
## 242   2020-10-28          East of England     12
## 243   2020-10-29          East of England     10
## 244   2020-10-30          East of England     12
## 245   2020-10-31          East of England     15
## 246   2020-11-01          East of England     14
## 247   2020-11-02          East of England      9
## 248   2020-11-03          East of England     14
## 249   2020-11-04          East of England     11
## 250   2020-11-05          East of England     12
## 251   2020-11-06          East of England     18
## 252   2020-11-07          East of England     10
## 253   2020-11-08          East of England     13
## 254   2020-11-09          East of England     16
## 255   2020-11-10          East of England     26
## 256   2020-11-11          East of England     14
## 257   2020-11-12          East of England     14
## 258   2020-11-13          East of England     21
## 259   2020-11-14          East of England     19
## 260   2020-11-15          East of England     13
## 261   2020-11-16          East of England     11
## 262   2020-11-17          East of England     17
## 263   2020-11-18          East of England     19
## 264   2020-11-19          East of England     23
## 265   2020-11-20          East of England     24
## 266   2020-11-21          East of England     19
## 267   2020-11-22          East of England     21
## 268   2020-11-23          East of England     18
## 269   2020-11-24          East of England     21
## 270   2020-11-25          East of England     19
## 271   2020-11-26          East of England     19
## 272   2020-11-27          East of England     14
## 273   2020-11-28          East of England     28
## 274   2020-11-29          East of England     19
## 275   2020-11-30          East of England     22
## 276   2020-12-01          East of England     26
## 277   2020-12-02          East of England     18
## 278   2020-12-03          East of England     24
## 279   2020-12-04          East of England     25
## 280   2020-12-05          East of England     25
## 281   2020-12-06          East of England     21
## 282   2020-12-07          East of England     16
## 283   2020-12-08          East of England     26
## 284   2020-12-09          East of England     19
## 285   2020-12-10          East of England     32
## 286   2020-12-11          East of England     32
## 287   2020-12-12          East of England     27
## 288   2020-12-13          East of England     25
## 289   2020-12-14          East of England     32
## 290   2020-12-15          East of England     35
## 291   2020-12-16          East of England     29
## 292   2020-12-17          East of England     42
## 293   2020-12-18          East of England     44
## 294   2020-12-19          East of England     54
## 295   2020-12-20          East of England     51
## 296   2020-12-21          East of England     66
## 297   2020-12-22          East of England     52
## 298   2020-12-23          East of England     61
## 299   2020-12-24          East of England     61
## 300   2020-12-25          East of England     57
## 301   2020-12-26          East of England     62
## 302   2020-12-27          East of England     54
## 303   2020-12-28          East of England     71
## 304   2020-12-29          East of England     53
## 305   2020-12-30          East of England     76
## 306   2020-12-31          East of England     82
## 307   2021-01-01          East of England     89
## 308   2021-01-02          East of England     66
## 309   2021-01-03          East of England     78
## 310   2021-01-04          East of England     87
## 311   2021-01-05          East of England    102
## 312   2021-01-06          East of England     99
## 313   2021-01-07          East of England    116
## 314   2021-01-08          East of England     95
## 315   2021-01-09          East of England    129
## 316   2021-01-10          East of England    123
## 317   2021-01-11          East of England    123
## 318   2021-01-12          East of England    128
## 319   2021-01-13          East of England    126
## 320   2021-01-14          East of England    124
## 321   2021-01-15          East of England    117
## 322   2021-01-16          East of England    128
## 323   2021-01-17          East of England    128
## 324   2021-01-18          East of England    119
## 325   2021-01-19          East of England    127
## 326   2021-01-20          East of England    147
## 327   2021-01-21          East of England    130
## 328   2021-01-22          East of England    118
## 329   2021-01-23          East of England    102
## 330   2021-01-24          East of England    100
## 331   2021-01-25          East of England    111
## 332   2021-01-26          East of England     86
## 333   2021-01-27          East of England     92
## 334   2021-01-28          East of England    109
## 335   2021-01-29          East of England     92
## 336   2021-01-30          East of England     82
## 337   2021-01-31          East of England     71
## 338   2021-02-01          East of England     61
## 339   2021-02-02          East of England     71
## 340   2021-02-03          East of England     77
## 341   2021-02-04          East of England     74
## 342   2021-02-05          East of England     64
## 343   2021-02-06          East of England     72
## 344   2021-02-07          East of England     60
## 345   2021-02-08          East of England     73
## 346   2021-02-09          East of England     60
## 347   2021-02-10          East of England     49
## 348   2021-02-11          East of England     48
## 349   2021-02-12          East of England     37
## 350   2021-02-13          East of England     30
## 351   2021-02-14          East of England     16
## 352   2021-02-15          East of England      4
## 353   2020-03-01                   London      0
## 354   2020-03-02                   London      0
## 355   2020-03-03                   London      0
## 356   2020-03-04                   London      0
## 357   2020-03-05                   London      0
## 358   2020-03-06                   London      1
## 359   2020-03-07                   London      0
## 360   2020-03-08                   London      0
## 361   2020-03-09                   London      1
## 362   2020-03-10                   London      0
## 363   2020-03-11                   London      5
## 364   2020-03-12                   London      6
## 365   2020-03-13                   London     10
## 366   2020-03-14                   London     13
## 367   2020-03-15                   London      9
## 368   2020-03-16                   London     15
## 369   2020-03-17                   London     23
## 370   2020-03-18                   London     28
## 371   2020-03-19                   London     25
## 372   2020-03-20                   London     44
## 373   2020-03-21                   London     49
## 374   2020-03-22                   London     54
## 375   2020-03-23                   London     63
## 376   2020-03-24                   London     86
## 377   2020-03-25                   London    112
## 378   2020-03-26                   London    130
## 379   2020-03-27                   London    130
## 380   2020-03-28                   London    123
## 381   2020-03-29                   London    145
## 382   2020-03-30                   London    151
## 383   2020-03-31                   London    183
## 384   2020-04-01                   London    202
## 385   2020-04-02                   London    191
## 386   2020-04-03                   London    199
## 387   2020-04-04                   London    231
## 388   2020-04-05                   London    195
## 389   2020-04-06                   London    198
## 390   2020-04-07                   London    220
## 391   2020-04-08                   London    239
## 392   2020-04-09                   London    207
## 393   2020-04-10                   London    171
## 394   2020-04-11                   London    178
## 395   2020-04-12                   London    159
## 396   2020-04-13                   London    166
## 397   2020-04-14                   London    143
## 398   2020-04-15                   London    143
## 399   2020-04-16                   London    140
## 400   2020-04-17                   London    101
## 401   2020-04-18                   London    101
## 402   2020-04-19                   London    103
## 403   2020-04-20                   London     96
## 404   2020-04-21                   London     96
## 405   2020-04-22                   London    109
## 406   2020-04-23                   London     77
## 407   2020-04-24                   London     71
## 408   2020-04-25                   London     58
## 409   2020-04-26                   London     53
## 410   2020-04-27                   London     52
## 411   2020-04-28                   London     44
## 412   2020-04-29                   London     45
## 413   2020-04-30                   London     40
## 414   2020-05-01                   London     41
## 415   2020-05-02                   London     41
## 416   2020-05-03                   London     36
## 417   2020-05-04                   London     30
## 418   2020-05-05                   London     25
## 419   2020-05-06                   London     37
## 420   2020-05-07                   London     37
## 421   2020-05-08                   London     31
## 422   2020-05-09                   London     23
## 423   2020-05-10                   London     26
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## 1446  2020-04-07               North West    136
## 1447  2020-04-08               North West    127
## 1448  2020-04-09               North West    119
## 1449  2020-04-10               North West    117
## 1450  2020-04-11               North West    138
## 1451  2020-04-12               North West    125
## 1452  2020-04-13               North West    130
## 1453  2020-04-14               North West    130
## 1454  2020-04-15               North West    114
## 1455  2020-04-16               North West    135
## 1456  2020-04-17               North West     98
## 1457  2020-04-18               North West    113
## 1458  2020-04-19               North West     71
## 1459  2020-04-20               North West     83
## 1460  2020-04-21               North West     76
## 1461  2020-04-22               North West     87
## 1462  2020-04-23               North West     85
## 1463  2020-04-24               North West     67
## 1464  2020-04-25               North West     67
## 1465  2020-04-26               North West     55
## 1466  2020-04-27               North West     54
## 1467  2020-04-28               North West     57
## 1468  2020-04-29               North West     64
## 1469  2020-04-30               North West     60
## 1470  2020-05-01               North West     45
## 1471  2020-05-02               North West     56
## 1472  2020-05-03               North West     55
## 1473  2020-05-04               North West     48
## 1474  2020-05-05               North West     49
## 1475  2020-05-06               North West     44
## 1476  2020-05-07               North West     50
## 1477  2020-05-08               North West     43
## 1478  2020-05-09               North West     31
## 1479  2020-05-10               North West     42
## 1480  2020-05-11               North West     35
## 1481  2020-05-12               North West     38
## 1482  2020-05-13               North West     25
## 1483  2020-05-14               North West     26
## 1484  2020-05-15               North West     33
## 1485  2020-05-16               North West     32
## 1486  2020-05-17               North West     24
## 1487  2020-05-18               North West     31
## 1488  2020-05-19               North West     35
## 1489  2020-05-20               North West     27
## 1490  2020-05-21               North West     28
## 1491  2020-05-22               North West     26
## 1492  2020-05-23               North West     31
## 1493  2020-05-24               North West     26
## 1494  2020-05-25               North West     31
## 1495  2020-05-26               North West     27
## 1496  2020-05-27               North West     27
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## 1501  2020-06-01               North West     12
## 1502  2020-06-02               North West     27
## 1503  2020-06-03               North West     22
## 1504  2020-06-04               North West     22
## 1505  2020-06-05               North West     16
## 1506  2020-06-06               North West     26
## 1507  2020-06-07               North West     20
## 1508  2020-06-08               North West     23
## 1509  2020-06-09               North West     17
## 1510  2020-06-10               North West     16
## 1511  2020-06-11               North West     16
## 1512  2020-06-12               North West     11
## 1513  2020-06-13               North West     10
## 1514  2020-06-14               North West     15
## 1515  2020-06-15               North West     16
## 1516  2020-06-16               North West     16
## 1517  2020-06-17               North West     13
## 1518  2020-06-18               North West     14
## 1519  2020-06-19               North West      7
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## 1521  2020-06-21               North West      8
## 1522  2020-06-22               North West     11
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## 1524  2020-06-24               North West     13
## 1525  2020-06-25               North West     15
## 1526  2020-06-26               North West      6
## 1527  2020-06-27               North West      7
## 1528  2020-06-28               North West      9
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## 1530  2020-06-30               North West      7
## 1531  2020-07-01               North West      3
## 1532  2020-07-02               North West      6
## 1533  2020-07-03               North West      7
## 1534  2020-07-04               North West      4
## 1535  2020-07-05               North West      6
## 1536  2020-07-06               North West      9
## 1537  2020-07-07               North West      8
## 1538  2020-07-08               North West      5
## 1539  2020-07-09               North West     10
## 1540  2020-07-10               North West      2
## 1541  2020-07-11               North West      5
## 1542  2020-07-12               North West      0
## 1543  2020-07-13               North West      6
## 1544  2020-07-14               North West      4
## 1545  2020-07-15               North West      5
## 1546  2020-07-16               North West      2
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## 1550  2020-07-20               North West      0
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## 1562  2020-08-01               North West      2
## 1563  2020-08-02               North West      1
## 1564  2020-08-03               North West      8
## 1565  2020-08-04               North West      3
## 1566  2020-08-05               North West      2
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## 1625  2020-10-03               North West     15
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## 1957  2020-09-13               South East      3
## 1958  2020-09-14               South East      1
## 1959  2020-09-15               South East      2
## 1960  2020-09-16               South East      2
## 1961  2020-09-17               South East      3
## 1962  2020-09-18               South East      1
## 1963  2020-09-19               South East      1
## 1964  2020-09-20               South East      0
## 1965  2020-09-21               South East      3
## 1966  2020-09-22               South East      0
## 1967  2020-09-23               South East      2
## 1968  2020-09-24               South East      1
## 1969  2020-09-25               South East      3
## 1970  2020-09-26               South East      2
## 1971  2020-09-27               South East      2
## 1972  2020-09-28               South East      6
## 1973  2020-09-29               South East      3
## 1974  2020-09-30               South East      4
## 1975  2020-10-01               South East      4
## 1976  2020-10-02               South East      2
## 1977  2020-10-03               South East      1
## 1978  2020-10-04               South East      1
## 1979  2020-10-05               South East      2
## 1980  2020-10-06               South East      1
## 1981  2020-10-07               South East      4
## 1982  2020-10-08               South East      1
## 1983  2020-10-09               South East      1
## 1984  2020-10-10               South East      3
## 1985  2020-10-11               South East      3
## 1986  2020-10-12               South East      4
## 1987  2020-10-13               South East      2
## 1988  2020-10-14               South East      2
## 1989  2020-10-15               South East      3
## 1990  2020-10-16               South East      2
## 1991  2020-10-17               South East      3
## 1992  2020-10-18               South East      4
## 1993  2020-10-19               South East      7
## 1994  2020-10-20               South East      8
## 1995  2020-10-21               South East      9
## 1996  2020-10-22               South East      5
## 1997  2020-10-23               South East      7
## 1998  2020-10-24               South East      5
## 1999  2020-10-25               South East      9
## 2000  2020-10-26               South East     13
## 2001  2020-10-27               South East     10
## 2002  2020-10-28               South East     10
## 2003  2020-10-29               South East      7
## 2004  2020-10-30               South East      6
## 2005  2020-10-31               South East     15
## 2006  2020-11-01               South East     18
## 2007  2020-11-02               South East     13
## 2008  2020-11-03               South East     16
## 2009  2020-11-04               South East     10
## 2010  2020-11-05               South East     10
## 2011  2020-11-06               South East     16
## 2012  2020-11-07               South East     17
## 2013  2020-11-08               South East     18
## 2014  2020-11-09               South East     19
## 2015  2020-11-10               South East     20
## 2016  2020-11-11               South East     20
## 2017  2020-11-12               South East     20
## 2018  2020-11-13               South East     12
## 2019  2020-11-14               South East     24
## 2020  2020-11-15               South East     25
## 2021  2020-11-16               South East     22
## 2022  2020-11-17               South East     23
## 2023  2020-11-18               South East     26
## 2024  2020-11-19               South East     21
## 2025  2020-11-20               South East     18
## 2026  2020-11-21               South East     23
## 2027  2020-11-22               South East     30
## 2028  2020-11-23               South East     29
## 2029  2020-11-24               South East     26
## 2030  2020-11-25               South East     42
## 2031  2020-11-26               South East     30
## 2032  2020-11-27               South East     31
## 2033  2020-11-28               South East     24
## 2034  2020-11-29               South East     37
## 2035  2020-11-30               South East     23
## 2036  2020-12-01               South East     29
## 2037  2020-12-02               South East     33
## 2038  2020-12-03               South East     36
## 2039  2020-12-04               South East     41
## 2040  2020-12-05               South East     36
## 2041  2020-12-06               South East     32
## 2042  2020-12-07               South East     25
## 2043  2020-12-08               South East     43
## 2044  2020-12-09               South East     44
## 2045  2020-12-10               South East     38
## 2046  2020-12-11               South East     48
## 2047  2020-12-12               South East     40
## 2048  2020-12-13               South East     41
## 2049  2020-12-14               South East     38
## 2050  2020-12-15               South East     51
## 2051  2020-12-16               South East     45
## 2052  2020-12-17               South East     54
## 2053  2020-12-18               South East     48
## 2054  2020-12-19               South East     43
## 2055  2020-12-20               South East     57
## 2056  2020-12-21               South East     66
## 2057  2020-12-22               South East     62
## 2058  2020-12-23               South East     70
## 2059  2020-12-24               South East     56
## 2060  2020-12-25               South East     71
## 2061  2020-12-26               South East     75
## 2062  2020-12-27               South East     76
## 2063  2020-12-28               South East     81
## 2064  2020-12-29               South East     78
## 2065  2020-12-30               South East     92
## 2066  2020-12-31               South East     92
## 2067  2021-01-01               South East     60
## 2068  2021-01-02               South East     94
## 2069  2021-01-03               South East     79
## 2070  2021-01-04               South East    106
## 2071  2021-01-05               South East    107
## 2072  2021-01-06               South East    121
## 2073  2021-01-07               South East    116
## 2074  2021-01-08               South East    125
## 2075  2021-01-09               South East    115
## 2076  2021-01-10               South East    125
## 2077  2021-01-11               South East    128
## 2078  2021-01-12               South East    169
## 2079  2021-01-13               South East    133
## 2080  2021-01-14               South East    138
## 2081  2021-01-15               South East    125
## 2082  2021-01-16               South East    153
## 2083  2021-01-17               South East    165
## 2084  2021-01-18               South East    151
## 2085  2021-01-19               South East    154
## 2086  2021-01-20               South East    134
## 2087  2021-01-21               South East    132
## 2088  2021-01-22               South East    129
## 2089  2021-01-23               South East    121
## 2090  2021-01-24               South East    115
## 2091  2021-01-25               South East    112
## 2092  2021-01-26               South East    130
## 2093  2021-01-27               South East    111
## 2094  2021-01-28               South East    127
## 2095  2021-01-29               South East    107
## 2096  2021-01-30               South East     92
## 2097  2021-01-31               South East     93
## 2098  2021-02-01               South East     94
## 2099  2021-02-02               South East     81
## 2100  2021-02-03               South East     95
## 2101  2021-02-04               South East     58
## 2102  2021-02-05               South East     68
## 2103  2021-02-06               South East     73
## 2104  2021-02-07               South East     63
## 2105  2021-02-08               South East     66
## 2106  2021-02-09               South East     35
## 2107  2021-02-10               South East     43
## 2108  2021-02-11               South East     55
## 2109  2021-02-12               South East     35
## 2110  2021-02-13               South East     27
## 2111  2021-02-14               South East     30
## 2112  2021-02-15               South East      9
## 2113  2020-03-01               South West      0
## 2114  2020-03-02               South West      0
## 2115  2020-03-03               South West      0
## 2116  2020-03-04               South West      0
## 2117  2020-03-05               South West      0
## 2118  2020-03-06               South West      0
## 2119  2020-03-07               South West      0
## 2120  2020-03-08               South West      0
## 2121  2020-03-09               South West      0
## 2122  2020-03-10               South West      0
## 2123  2020-03-11               South West      1
## 2124  2020-03-12               South West      0
## 2125  2020-03-13               South West      0
## 2126  2020-03-14               South West      1
## 2127  2020-03-15               South West      0
## 2128  2020-03-16               South West      0
## 2129  2020-03-17               South West      2
## 2130  2020-03-18               South West      2
## 2131  2020-03-19               South West      4
## 2132  2020-03-20               South West      3
## 2133  2020-03-21               South West      6
## 2134  2020-03-22               South West      7
## 2135  2020-03-23               South West      8
## 2136  2020-03-24               South West      7
## 2137  2020-03-25               South West      9
## 2138  2020-03-26               South West     11
## 2139  2020-03-27               South West     13
## 2140  2020-03-28               South West     21
## 2141  2020-03-29               South West     18
## 2142  2020-03-30               South West     23
## 2143  2020-03-31               South West     23
## 2144  2020-04-01               South West     21
## 2145  2020-04-02               South West     23
## 2146  2020-04-03               South West     30
## 2147  2020-04-04               South West     42
## 2148  2020-04-05               South West     32
## 2149  2020-04-06               South West     34
## 2150  2020-04-07               South West     39
## 2151  2020-04-08               South West     47
## 2152  2020-04-09               South West     24
## 2153  2020-04-10               South West     46
## 2154  2020-04-11               South West     43
## 2155  2020-04-12               South West     23
## 2156  2020-04-13               South West     27
## 2157  2020-04-14               South West     24
## 2158  2020-04-15               South West     32
## 2159  2020-04-16               South West     29
## 2160  2020-04-17               South West     33
## 2161  2020-04-18               South West     25
## 2162  2020-04-19               South West     31
## 2163  2020-04-20               South West     26
## 2164  2020-04-21               South West     26
## 2165  2020-04-22               South West     23
## 2166  2020-04-23               South West     17
## 2167  2020-04-24               South West     19
## 2168  2020-04-25               South West     15
## 2169  2020-04-26               South West     27
## 2170  2020-04-27               South West     13
## 2171  2020-04-28               South West     17
## 2172  2020-04-29               South West     15
## 2173  2020-04-30               South West     26
## 2174  2020-05-01               South West      6
## 2175  2020-05-02               South West      7
## 2176  2020-05-03               South West     10
## 2177  2020-05-04               South West     17
## 2178  2020-05-05               South West     14
## 2179  2020-05-06               South West     19
## 2180  2020-05-07               South West     16
## 2181  2020-05-08               South West      6
## 2182  2020-05-09               South West     11
## 2183  2020-05-10               South West      5
## 2184  2020-05-11               South West      8
## 2185  2020-05-12               South West      7
## 2186  2020-05-13               South West      7
## 2187  2020-05-14               South West      6
## 2188  2020-05-15               South West      4
## 2189  2020-05-16               South West      4
## 2190  2020-05-17               South West      6
## 2191  2020-05-18               South West      4
## 2192  2020-05-19               South West      6
## 2193  2020-05-20               South West      1
## 2194  2020-05-21               South West      9
## 2195  2020-05-22               South West      7
## 2196  2020-05-23               South West      6
## 2197  2020-05-24               South West      3
## 2198  2020-05-25               South West      8
## 2199  2020-05-26               South West     11
## 2200  2020-05-27               South West      5
## 2201  2020-05-28               South West     10
## 2202  2020-05-29               South West      7
## 2203  2020-05-30               South West      3
## 2204  2020-05-31               South West      2
## 2205  2020-06-01               South West      7
## 2206  2020-06-02               South West      2
## 2207  2020-06-03               South West      7
## 2208  2020-06-04               South West      2
## 2209  2020-06-05               South West      2
## 2210  2020-06-06               South West      1
## 2211  2020-06-07               South West      3
## 2212  2020-06-08               South West      3
## 2213  2020-06-09               South West      0
## 2214  2020-06-10               South West      1
## 2215  2020-06-11               South West      2
## 2216  2020-06-12               South West      2
## 2217  2020-06-13               South West      2
## 2218  2020-06-14               South West      0
## 2219  2020-06-15               South West      2
## 2220  2020-06-16               South West      2
## 2221  2020-06-17               South West      0
## 2222  2020-06-18               South West      0
## 2223  2020-06-19               South West      0
## 2224  2020-06-20               South West      2
## 2225  2020-06-21               South West      0
## 2226  2020-06-22               South West      1
## 2227  2020-06-23               South West      1
## 2228  2020-06-24               South West      1
## 2229  2020-06-25               South West      0
## 2230  2020-06-26               South West      3
## 2231  2020-06-27               South West      0
## 2232  2020-06-28               South West      0
## 2233  2020-06-29               South West      1
## 2234  2020-06-30               South West      0
## 2235  2020-07-01               South West      0
## 2236  2020-07-02               South West      0
## 2237  2020-07-03               South West      0
## 2238  2020-07-04               South West      0
## 2239  2020-07-05               South West      1
## 2240  2020-07-06               South West      0
## 2241  2020-07-07               South West      0
## 2242  2020-07-08               South West      2
## 2243  2020-07-09               South West      0
## 2244  2020-07-10               South West      1
## 2245  2020-07-11               South West      0
## 2246  2020-07-12               South West      0
## 2247  2020-07-13               South West      1
## 2248  2020-07-14               South West      0
## 2249  2020-07-15               South West      0
## 2250  2020-07-16               South West      0
## 2251  2020-07-17               South West      1
## 2252  2020-07-18               South West      0
## 2253  2020-07-19               South West      0
## 2254  2020-07-20               South West      0
## 2255  2020-07-21               South West      0
## 2256  2020-07-22               South West      0
## 2257  2020-07-23               South West      0
## 2258  2020-07-24               South West      0
## 2259  2020-07-25               South West      0
## 2260  2020-07-26               South West      0
## 2261  2020-07-27               South West      0
## 2262  2020-07-28               South West      0
## 2263  2020-07-29               South West      0
## 2264  2020-07-30               South West      1
## 2265  2020-07-31               South West      0
## 2266  2020-08-01               South West      0
## 2267  2020-08-02               South West      0
## 2268  2020-08-03               South West      0
## 2269  2020-08-04               South West      0
## 2270  2020-08-05               South West      0
## 2271  2020-08-06               South West      0
## 2272  2020-08-07               South West      0
## 2273  2020-08-08               South West      0
## 2274  2020-08-09               South West      0
## 2275  2020-08-10               South West      0
## 2276  2020-08-11               South West      0
## 2277  2020-08-12               South West      0
## 2278  2020-08-13               South West      0
## 2279  2020-08-14               South West      1
## 2280  2020-08-15               South West      0
## 2281  2020-08-16               South West      0
## 2282  2020-08-17               South West      2
## 2283  2020-08-18               South West      0
## 2284  2020-08-19               South West      0
## 2285  2020-08-20               South West      0
## 2286  2020-08-21               South West      0
## 2287  2020-08-22               South West      0
## 2288  2020-08-23               South West      0
## 2289  2020-08-24               South West      0
## 2290  2020-08-25               South West      1
## 2291  2020-08-26               South West      0
## 2292  2020-08-27               South West      1
## 2293  2020-08-28               South West      0
## 2294  2020-08-29               South West      0
## 2295  2020-08-30               South West      0
## 2296  2020-08-31               South West      0
## 2297  2020-09-01               South West      0
## 2298  2020-09-02               South West      0
## 2299  2020-09-03               South West      0
## 2300  2020-09-04               South West      0
## 2301  2020-09-05               South West      0
## 2302  2020-09-06               South West      0
## 2303  2020-09-07               South West      0
## 2304  2020-09-08               South West      1
## 2305  2020-09-09               South West      0
## 2306  2020-09-10               South West      0
## 2307  2020-09-11               South West      0
## 2308  2020-09-12               South West      0
## 2309  2020-09-13               South West      1
## 2310  2020-09-14               South West      0
## 2311  2020-09-15               South West      0
## 2312  2020-09-16               South West      0
## 2313  2020-09-17               South West      1
## 2314  2020-09-18               South West      0
## 2315  2020-09-19               South West      0
## 2316  2020-09-20               South West      1
## 2317  2020-09-21               South West      0
## 2318  2020-09-22               South West      0
## 2319  2020-09-23               South West      0
## 2320  2020-09-24               South West      1
## 2321  2020-09-25               South West      0
## 2322  2020-09-26               South West      0
## 2323  2020-09-27               South West      0
## 2324  2020-09-28               South West      0
## 2325  2020-09-29               South West      0
## 2326  2020-09-30               South West      0
## 2327  2020-10-01               South West      0
## 2328  2020-10-02               South West      1
## 2329  2020-10-03               South West      0
## 2330  2020-10-04               South West      0
## 2331  2020-10-05               South West      0
## 2332  2020-10-06               South West      1
## 2333  2020-10-07               South West      0
## 2334  2020-10-08               South West      1
## 2335  2020-10-09               South West      1
## 2336  2020-10-10               South West      0
## 2337  2020-10-11               South West      4
## 2338  2020-10-12               South West      2
## 2339  2020-10-13               South West      0
## 2340  2020-10-14               South West      3
## 2341  2020-10-15               South West      1
## 2342  2020-10-16               South West      2
## 2343  2020-10-17               South West      8
## 2344  2020-10-18               South West      2
## 2345  2020-10-19               South West      2
## 2346  2020-10-20               South West      3
## 2347  2020-10-21               South West      6
## 2348  2020-10-22               South West      6
## 2349  2020-10-23               South West      5
## 2350  2020-10-24               South West      5
## 2351  2020-10-25               South West      5
## 2352  2020-10-26               South West      7
## 2353  2020-10-27               South West      6
## 2354  2020-10-28               South West      8
## 2355  2020-10-29               South West     11
## 2356  2020-10-30               South West      8
## 2357  2020-10-31               South West      4
## 2358  2020-11-01               South West      5
## 2359  2020-11-02               South West     11
## 2360  2020-11-03               South West      7
## 2361  2020-11-04               South West      8
## 2362  2020-11-05               South West      5
## 2363  2020-11-06               South West     11
## 2364  2020-11-07               South West     10
## 2365  2020-11-08               South West     10
## 2366  2020-11-09               South West     12
## 2367  2020-11-10               South West      6
## 2368  2020-11-11               South West     13
## 2369  2020-11-12               South West     17
## 2370  2020-11-13               South West      9
## 2371  2020-11-14               South West      8
## 2372  2020-11-15               South West     16
## 2373  2020-11-16               South West     18
## 2374  2020-11-17               South West     17
## 2375  2020-11-18               South West     26
## 2376  2020-11-19               South West     15
## 2377  2020-11-20               South West     25
## 2378  2020-11-21               South West     25
## 2379  2020-11-22               South West     24
## 2380  2020-11-23               South West     14
## 2381  2020-11-24               South West     20
## 2382  2020-11-25               South West     25
## 2383  2020-11-26               South West     16
## 2384  2020-11-27               South West     21
## 2385  2020-11-28               South West     35
## 2386  2020-11-29               South West     15
## 2387  2020-11-30               South West     22
## 2388  2020-12-01               South West     19
## 2389  2020-12-02               South West     15
## 2390  2020-12-03               South West     14
## 2391  2020-12-04               South West     20
## 2392  2020-12-05               South West     17
## 2393  2020-12-06               South West     13
## 2394  2020-12-07               South West     16
## 2395  2020-12-08               South West     19
## 2396  2020-12-09               South West     21
## 2397  2020-12-10               South West     20
## 2398  2020-12-11               South West     20
## 2399  2020-12-12               South West     15
## 2400  2020-12-13               South West     19
## 2401  2020-12-14               South West     20
## 2402  2020-12-15               South West     20
## 2403  2020-12-16               South West      9
## 2404  2020-12-17               South West     26
## 2405  2020-12-18               South West     11
## 2406  2020-12-19               South West     22
## 2407  2020-12-20               South West     19
## 2408  2020-12-21               South West     22
## 2409  2020-12-22               South West     10
## 2410  2020-12-23               South West     16
## 2411  2020-12-24               South West     18
## 2412  2020-12-25               South West     19
## 2413  2020-12-26               South West     24
## 2414  2020-12-27               South West     24
## 2415  2020-12-28               South West     21
## 2416  2020-12-29               South West     20
## 2417  2020-12-30               South West     17
## 2418  2020-12-31               South West     27
## 2419  2021-01-01               South West     29
## 2420  2021-01-02               South West     24
## 2421  2021-01-03               South West     28
## 2422  2021-01-04               South West     30
## 2423  2021-01-05               South West     31
## 2424  2021-01-06               South West     24
## 2425  2021-01-07               South West     29
## 2426  2021-01-08               South West     33
## 2427  2021-01-09               South West     26
## 2428  2021-01-10               South West     31
## 2429  2021-01-11               South West     36
## 2430  2021-01-12               South West     48
## 2431  2021-01-13               South West     40
## 2432  2021-01-14               South West     32
## 2433  2021-01-15               South West     44
## 2434  2021-01-16               South West     54
## 2435  2021-01-17               South West     32
## 2436  2021-01-18               South West     42
## 2437  2021-01-19               South West     43
## 2438  2021-01-20               South West     62
## 2439  2021-01-21               South West     54
## 2440  2021-01-22               South West     57
## 2441  2021-01-23               South West     52
## 2442  2021-01-24               South West     59
## 2443  2021-01-25               South West     55
## 2444  2021-01-26               South West     42
## 2445  2021-01-27               South West     40
## 2446  2021-01-28               South West     48
## 2447  2021-01-29               South West     41
## 2448  2021-01-30               South West     36
## 2449  2021-01-31               South West     34
## 2450  2021-02-01               South West     28
## 2451  2021-02-02               South West     35
## 2452  2021-02-03               South West     31
## 2453  2021-02-04               South West     31
## 2454  2021-02-05               South West     24
## 2455  2021-02-06               South West     37
## 2456  2021-02-07               South West     33
## 2457  2021-02-08               South West     30
## 2458  2021-02-09               South West     29
## 2459  2021-02-10               South West     16
## 2460  2021-02-11               South West     18
## 2461  2021-02-12               South West     12
## 2462  2021-02-13               South West     14
## 2463  2021-02-14               South West      5
## 2464  2021-02-15               South West      2

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2021-02-16"

The completion date of the NHS Pathways data is Tuesday 16 Feb 2021.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 14 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 14 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -17.954  -15.382   -5.572    6.718   34.704  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 5.096e+00  7.095e-02   71.83   <2e-16 ***
## note_lag    1.245e-05  1.245e-06   10.00   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 217.172)
## 
##     Null deviance: 75336  on 299  degrees of freedom
## Residual deviance: 59475  on 298  degrees of freedom
##   (14 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 5

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##  163.444846    1.000012
exp(confint(lag_mod))
##                 2.5 %     97.5 %
## (Intercept) 141.83405 187.335621
## note_lag      1.00001   1.000015

Rsq(lag_mod)
## [1] 0.2105332

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                             sysname 
##                                                                                            "Darwin" 
##                                                                                             release 
##                                                                                            "19.6.0" 
##                                                                                             version 
## "Darwin Kernel Version 19.6.0: Tue Jan 12 22:13:05 PST 2021; root:xnu-6153.141.16~1/RELEASE_X86_64" 
##                                                                                            nodename 
##                                                                           "Mac-1613556564235.local" 
##                                                                                             machine 
##                                                                                            "x86_64" 
##                                                                                               login 
##                                                                                              "root" 
##                                                                                                user 
##                                                                                            "runner" 
##                                                                                      effective_user 
##                                                                                            "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin17.0     
## arch           x86_64                      
## os             darwin17.0                  
## system         x86_64, darwin17.0          
## status                                     
## major          4                           
## minor          0.4                         
## year           2021                        
## month          02                          
## day            15                          
## svn rev        80002                       
## language       R                           
## version.string R version 4.0.4 (2021-02-15)
## nickname       Lost Library Book

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 4.0.4 (2021-02-15)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.7
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.5     ggpubr_0.4.0         lubridate_1.7.9.2   
##  [4] chngpt_2020.10-12    cyphr_1.1.0          DT_0.17             
##  [7] kableExtra_1.3.2     janitor_2.1.0        remotes_2.2.0       
## [10] projections_0.5.2    earlyR_0.0.5         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.3      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.6          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.1        stringr_1.4.0       
## [22] dplyr_1.0.4          purrr_0.3.4          readr_1.4.0         
## [25] tidyr_1.1.2          tibble_3.0.6         ggplot2_3.3.3       
## [28] tidyverse_1.3.0      here_1.0.1           reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] minqa_1.2.4       colorspace_2.0-0  selectr_0.4-2     ggsignif_0.6.0   
##  [5] ellipsis_0.3.1    rprojroot_2.0.2   snakecase_0.11.0  fs_1.5.0         
##  [9] rstudioapi_0.13   farver_2.0.3      fansi_0.4.2       splines_4.0.4    
## [13] knitr_1.31        jsonlite_1.7.2    nloptr_1.2.2.2    broom_0.7.4      
## [17] dbplyr_2.1.0      compiler_4.0.4    httr_1.4.2        backports_1.2.1  
## [21] assertthat_0.2.1  Matrix_1.3-2      cli_2.3.0         htmltools_0.5.1.1
## [25] tools_4.0.4       gtable_0.3.0      glue_1.4.2        Rcpp_1.0.6       
## [29] carData_3.0-4     cellranger_1.1.0  vctrs_0.3.6       nlme_3.1-152     
## [33] matchmaker_0.1.1  crosstalk_1.1.1   xfun_0.21         ps_1.5.0         
## [37] openxlsx_4.2.3    lme4_1.1-26       lifecycle_1.0.0   statmod_1.4.35   
## [41] rstatix_0.7.0     MASS_7.3-53       scales_1.1.1      hms_1.0.0        
## [45] parallel_4.0.4    sodium_1.1        yaml_2.2.1        curl_4.3         
## [49] gridExtra_2.3     stringi_1.5.3     highr_0.8         kyotil_2020.10-12
## [53] boot_1.3-26       zip_2.1.1         rlang_0.4.10      pkgconfig_2.0.3  
## [57] evaluate_0.14     lattice_0.20-41   labeling_0.4.2    htmlwidgets_1.5.3
## [61] cowplot_1.1.1     tidyselect_1.1.0  plyr_1.8.6        magrittr_2.0.1   
## [65] R6_2.5.0          generics_0.1.0    DBI_1.1.1         pillar_1.4.7     
## [69] haven_2.3.1       foreign_0.8-81    withr_2.4.1       mgcv_1.8-33      
## [73] survival_3.2-7    abind_1.4-5       modelr_0.1.8      crayon_1.4.1     
## [77] car_3.0-10        utf8_1.1.4        rmarkdown_2.6     viridis_0.5.1    
## [81] grid_4.0.4        readxl_1.3.1      data.table_1.13.6 reprex_1.0.0     
## [85] digest_0.6.27     webshot_0.5.2     munsell_0.5.0     viridisLite_0.3.0